Fermi-edge exciton-polaritons in doped semiconductor microcavities with finite hole mass

Abstract

The coupling between a 2D semiconductor quantum well and an optical cavity gives rise to combined light-matter excitations, the exciton-polaritons. These were usually measured when the conduction band is empty, making the single polariton physics a simple single-body problem. The situation is dramatically different in the presence of a finite conduction band population, where the creation or annihilation of a single exciton involves a many-body shakeup of the Fermi sea. Recent experiments in this regime revealed a strong modification of the exciton-polariton spectrum. Previous theoretical studies concerned with nonzero Fermi energy mostly relied on the approximation of an immobile valence band hole with infinite mass, which is appropriate for low-mobility samples only; for high-mobility samples, one needs to consider a mobile hole with large but finite mass. To bridge this gap we present an analytical diagrammatic approach and tackle a model with shortranged (screened) electron-hole interaction, studying it in two complementary regimes. We find that the finite hole mass has opposite effects on the exciton-polariton spectra in the two regimes: In the first, where the Fermi energy is much smaller than the exciton binding energy, excitonic features are enhanced by the finite mass. In the second regime, where the Fermi energy is much larger than the exciton binding energy, finite mass effects cut off the excitonic features in the polariton spectra, in qualitative agreement with recent experiments.

Spectra of heavy polarons and molecules coupled to a Fermi sea

“…A major difference is that the Monte-Carlo works extract the molecule solely from a pole in the two-particle propagator. The latter can be obtained from our recent work [34], and we found essentially opposite behavior to the one presented here; e.g., for E b µ, there is a sharp feature related to the molecule, and a broad continuum at larger energies. However, in the present work we have argued that the molecule emerges as an incoherent ground-state feature in the single-particle propagator as well.…”

“…The general strategy is to reevaluate the frequency-domain diagrams of Fig. 3(b) for finite mass [37], and trace the modification of the logarithmic singularities [34,[48][49][50][51][52]. Our results hold to leading order in the mass ratio β = m/M only, but we expect them to be qualitatively correct all the way up to β 1.…”

“…where F denotes the Fourier transform, F(f )(Ω) = dtf (t) exp(iΩt), and f and g are any two well-behaved functions; for more details, see Appendix B.2 of Ref. [34]. There is, however, a quicker way to arrive at the results: one can combine the impurity interacting with a forward propagating electron into a "bold" propagator of the form…”

“…Following Ref. [34], one can either work in the time or frequency domain, employing different approximations [37]. In particular, for small ω + E B , close to the molecular threshold, we find [44]…”

Many-body theory of optical absorption in doped two-dimensional semiconductors

“…Based on concepts related to the Fermi-polaron approach, the Fermi-edge singularity associated with optical transitions in doped materials in the large exciton mass limit can also be studied. In particular, the Mahan-Noziéres-De Dominicis (MND) theory provides a framework to study the doping dependence of optical lineshapes in a dense electron gas [11,12,[29][30][31][32][33][34][35][36]. Traditionally, the MND model is used to study an infinitemass hole immersed in a Fermi sea in conjunction with an electron-hole scattering potential to explain the origin of edge singularity behavior.…”